The area bounded by the coordinate axes and normal to the curve y=logex at the point P (1, 0), is

# The area bounded by the coordinate axes and normal to the curve $y={\mathrm{log}}_{e}x$ at the point , is

1. A

1 sq. unit

2. B

2 sq. units

3. C

$\frac{1}{2}$ sq. unit

4. D

none of these

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

We have,

$y={\mathrm{log}}_{e}x⇒\frac{dy}{dx}=\frac{1}{x}⇒{\left(\frac{dy}{dx}\right)}_{p}=1$

The equation of the normal at (1, 0) is

$y-0=-1\left(x-1\right)⇒x+y=1$

Clearly, it makes a triangle of area $\frac{1}{2}$ sq. unit with the

coordinate axes.

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)